A rectangular box has a base that is 4 times as long as it is wide. The sum of the height and the girth of the box is 200 feet. (a) Express the volume V of the box as a function of its width w. Determine the domain of V (w).

(a)

(b)

Step-by-step explanation:

Let's call the length of the box L, the width W and the height H. Then, we can write the following equations:

"A rectangular box has a base that is 4 times as long as it is wide"

"The sum of the height and the girth of the box is 200 feet"

The volume of the box is given by:

Using the L and H values from the equations above, we have:

The domain of V(W) is all positive values of W that gives a positive value for the volume (because a negative value for the volume or for the width doesn't make sense).

So to find where V(W) > 0, let's find first when V(W) = 0:

The volume is zero when W = 0 or W = 100.

For positive values of W ≤ 100, the term W^2 is positive, but the term (W - 100) is negative, then we would have a negative volume.

For positive values of W > 100, both terms W^2 and (W - 100) would be positive, giving a positive volume.

So the domain of V(W) is W > 100.

step-by-step explanation:

given that there are two triangles j'k'l' and jkl>

the former is got by dilating the second one.

when drawn on a grid, (graph paper) coordinates of vertices of first triangle is

(6,12)j, (9,6)k and (12,9)l

side jk has length = distance between j and k

=

side j'k'=distance between j' and k'

=

ie j'k'l' has sides 1/3 of that of corresponding sides of jkl.

hence scale factor of 1/3 is used to get j'k'l'from jkl